Three-body model forp-wave pion-O16scattering

A calculation of the elastic scattering of mesons from ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ is performed, using a modification of the first-order multiple scattering theory of Kerman, McManus, and Thaler, in which Pauli blocking effects are omitted from the $\tau$ operator. The modified $\tau$ operator is calculated in a three-body model, in which the struck nucleon is allowed to recoil in a Woods-Saxon nuclear shell model potential exerted by the remainder of the nucleus. The interaction between the meson and the struck nucleon is described by a separable potential. A set of coupled differential equations that describe the elastic and the excited channel wave functions is derived by approximating the shell model binding potential in the excited states of the nucleon as a potential for the meson-nucleon center of mass. This approximation is examined in detail. It is found that in the three-body model the bound states and the single particle resonances of the shell model potential alter the results significantly from those obtained in impulse approximation.